MAP estimation of piecewise constant digital signals

Abstract Given a noisy signal g , if we have a probabilistic model for the ensemble of possible (non-noisy) signals f and a probabilistic model for the noise, we can in principle find the f that most likely gave rise to g , using Bayes′ theorem; this most likely f is called the MAP ("maximum a posteriori") estimate of g . For discrete (digital) signals, the signal and noise probabilities can be arbitrary: it is not necessary to assume standard probability densities (e.g., Gaussian), which are unrealistic in many situations. However, MAP estimation is not commonly used even for digital signals, because the size of the set of possible f s is often exponential. In this paper we show, for piecewise constant f s, how the most likely f can be found using dynamic programming techniques that require only polynomial space and time. We also illustrate the performance of MAP estimation in recovering parameters of a simple signal or ensemble of signals in the presence of various types of noise.